Answer:
   
   Most rishonim (medieval halachic authorities) considered Christianity
   to be avodah zarah. A notable exception were the Tosafists. They felt
   that the trinity is shutfus (assigning partners to G-d). That the
   Father is the Creater, and identiable with the Jewish G-d, and the
   other persons of the trinity are minor deities that mediate. The
   practical distinction is that while Jews are prohibited from believing
   in shutfus, it is permitted to non-Jews under the covenant of Noah.
   
   The Tosafists are a major force in Ashkenazic ruling. On their ruling,
   many Orthodox Jews who work in jewelery sell crosses and crucafixes. A
   necessary factor is the assumption that the overwhelming majority of
   customers will be people who aren't Jewish (in the sense of
   peoplehood, not just religion). Others do not rule like the Tosafists.
   
   Another issue is whether the Tosafists' statement about the
   Catholicism of their day applies to any / some / most of the plurality
   of Christianities that exist today. For a pragmatic ruling, it's
   something you'd need to discuss with a rabbi.